In the parallelogram ABCD, the length of the diagonal BD, perpendicular to the side AB, is 6 cm
| February 28, 2021 | education
In the parallelogram ABCD, the length of the diagonal BD, perpendicular to the side AB, is 6 cm. The length of the AC is 2√22. Find the length of the side AD.
The diagonals of the parallelogram at the intersection point are divided in half, then AO = AC / 2 = 2 * √22 / 2 = √22 cm, BO = BD / 2 = 6/2 = 3 cm.
By condition, BD is perpendicular to AB, then the triangle ABO is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg AB.
AB ^ 2 = AO ^ 2 – BO ^ 2 = 22 – 9 = 13.
Triangle ABD is rectangular, in which we determine the length of the hypotenuse AD according to the Pythagorean theorem.
AD ^ 2 = AB ^ 2 + BD ^ 2 = 13 + 36 = 49.
AD = 7 cm.
Answer: The length of the side AD is 7 cm.
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